I find it strange that even in an alternative community, so many folks are so focused on getting money. Personally, I think if you are ignoring your privilege of coming from a place where you can easily make money, and going some place where people are not so privileged, and begging for money (rather than that bottle of water you need), your really a douche. Its easy to get what you need wherever, but to be fair, you dont need money.
Also, Mexico isnt really so poor (I mean the richest man in the world is a mexican, right?). The term third world really just refers to countries that didnt take a side in the cold war.
In any case, if you go there and beg, try to focus on the tourists at least. I never begged when I was living in Mexico/central America, and I had a great time. I made plenty of money busking for the tourists, and even landed a job (after a local tried begging me, and I only had 20 pesos.
And SlimJack, your chances of getting robbed or assaulted are way lower in Mexico than they are in the states.
I dunno, I guess my point is really that yes, You can technically get by in mexico (or other) "third world" countries by begging, but it kind of makes you an asshole, and a bad representation of Traveling folks. On the other hand, if you need something, as you said, people are friendly and open, just ask for what you need.